Finite Group Databasebeta

← Group #287284

Character table — Group #287284

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444488888888888888884444444448888888822448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ91111111111111111-1-111-1-1-1-11111-1-1-1-111111111-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11-1
χ101111111111111111-1-111-1-1-1-11111-1-1-1-111111111-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-11
χ111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1111-1
χ121111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-1-11
χ131111111111111111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-11-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-11
χ161111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-1111-1
χ17222222222-222-2-22-222-2-222-2-22222222200000000-2000000000000-2-2-2-200000000000000
χ18222222222-222-2-22-222-2-222-2-2-2-2-2-2-2-2-2-200000000-2000000000000222200000000000000
χ19222222222-222-2-22-2-2-2-2-2-2-2222222-2-2-2-2000000002000000000000-2-22200000000000000
χ20222222222-222-2-22-2-2-2-2-2-2-222-2-2-2-2222200000000200000000000022-2-200000000000000
χ2122222222-22-2-222-2222-2-2-2-2220000000000000000-222-2-222-2-20000000000000000000000
χ2222222222-22-2-222-2222-2-2-2-2220000000000000000-2-2-222-2-2220000000000000000000000
χ2322222222-22-2-222-22-2-2-2-222-2-20000000000000000222-2-2-2-2220000000000000000000000
χ2422222222-22-2-222-22-2-2-2-222-2-200000000000000002-2-22222-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i2000000002i2i−2i−2i000000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i200000000−2i−2i2i2i000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i-200000000−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i-2000000002i2i−2i−2i000000000000000000
χ2922-222-2-2-20200-2-2022-200002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20002-2002-2i2−i2i2−i2i2−i2i2−i200000000000000
χ3022-222-2-2-20200-2-2022-200002-2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000-2200-22−i2i2−i2i2i2−i2i2−i200000000000000
χ3122-222-2-2-20200-2-2022-200002-2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000-2200-22i2−i2i2−i2−i2i2−i2i200000000000000
χ3222-222-2-2-20200-2-2022-200002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20002-2002-2−i2i2−i2i2−i2i2−i2i200000000000000
χ3322-222-2-2-20200-2-202-220000-22i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20002-200-22−i2i2−i2i2i2−i2−i2i200000000000000
χ3422-222-2-2-20200-2-202-220000-22i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000-22002-2i2−i2i2−i2i2−i2−i2i200000000000000
χ3522-222-2-2-20200-2-202-220000-22−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000-22002-2−i2i2−i2i2−i2i2i2−i200000000000000
χ3622-222-2-2-20200-2-202-220000-22−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20002-200-22i2−i2i2−i2−i2i2i2−i200000000000000
χ3722-222-2-2-20-200220-22-20000-22i2i2−i2−i2i2i2−i2−i222−2−2−2−22202i−2i002i−2i002−2−22−i2i2−i2i200000000000000
χ3822-222-2-2-20-200220-22-20000-22i2i2−i2−i2i2i2−i2−i2−2−22222−2−20−2i2i00−2i2i00−222−2−i2i2−i2i200000000000000
χ3922-222-2-2-20-200220-22-20000-22−i2−i2i2i2−i2−i2i2i222−2−2−2−2220−2i2i00−2i2i002−2−22i2−i2i2−i200000000000000
χ4022-222-2-2-20-200220-22-20000-22−i2−i2i2i2−i2−i2i2i2−2−22222−2−202i−2i002i−2i00−222−2i2−i2i2−i200000000000000
χ4122-222-2-2-20-200220-2-2200002-2i2i2−i2−i2−i2−i2i2i222−2−2−2−22202i−2i00−2i2i00−222−2−i2i2i2−i200000000000000
χ4222-222-2-2-20-200220-2-2200002-2i2i2−i2−i2−i2−i2i2i2−2−22222−2−20−2i2i002i−2i002−2−22−i2i2i2−i200000000000000
χ4322-222-2-2-20-200220-2-2200002-2−i2−i2i2i2i2i2−i2−i222−2−2−2−2220−2i2i002i−2i00−222−2i2−i2−i2i200000000000000
χ4422-222-2-2-20-200220-2-2200002-2−i2−i2i2i2i2i2−i2−i2−2−22222−2−202i−2i00−2i2i002−2−22i2−i2−i2i200000000000000
χ452-222-22-2-22-22-22-2-22002-20000000000002i−2i2i−2i2i−2i2i−2i000000000000000002-2002i−2i00000000
χ462-222-22-2-22-22-22-2-22002-20000000000002i−2i2i−2i2i−2i2i−2i00000000000000000-2200−2i2i00000000
χ472-222-22-2-22-22-22-2-22002-2000000000000−2i2i−2i2i−2i2i−2i2i000000000000000002-200−2i2i00000000
χ482-222-22-2-22-22-22-2-22002-2000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000-22002i−2i00000000
χ492-222-22-2-2-22-22-222-2002-20000000000002-22-2-22-2200000000000000000002i−2i002i−2i000000
χ502-222-22-2-2-22-22-222-2002-20000000000002-22-2-22-220000000000000000000−2i2i00−2i2i000000
χ512-222-22-2-2-22-22-222-2002-2000000000000-22-222-22-200000000000000000002i−2i00−2i2i000000
χ522-222-22-2-2-22-22-222-2002-2000000000000-22-222-22-20000000000000000000−2i2i002i−2i000000
χ53444-4-4-44-440-4400-400000000000004-44-4000000000000000000000000000000000000000
χ54444-4-4-44-440-4400-40000000000000-44-44000000000000000000000000000000000000000
χ55444-4-4-44-4-404-40040000000004i−4i4i−4i0000000000000000000000000000000000000000000
χ56444-4-4-44-4-404-4004000000000−4i4i−4i4i0000000000000000000000000000000000000000000
χ5744-4-4-44-440000000000004i−4i0022−22−22222i2−2i2−2i22i2000000000000000000000000000000000000000
χ5844-4-4-44-440000000000004i−4i00−222222−22−2i22i22i2−2i2000000000000000000000000000000000000000
χ5944-4-4-44-44000000000000−4i4i0022−22−2222−2i22i22i2−2i2000000000000000000000000000000000000000
χ6044-4-4-44-44000000000000−4i4i00−222222−222i2−2i2−2i22i2000000000000000000000000000000000000000
χ614-444-44-4-4444-4-44-4-400-44000000000000000000000000000000000000000000000000000
χ624-444-44-4-4-4-4-444-44400-44000000000000000000000000000000000000000000000000000
χ634-44-44-4-4440-4-400400000000000000000000000000000000000000000000000000002i2−2i200
χ644-44-44-4-4440-4-40040000000000000000000000000000000000000000000000000000−2i22i200
χ654-44-44-4-44-404400-4000000000000000000000000000000000000000000000000002i2−2i20000
χ664-44-44-4-44-404400-400000000000000000000000000000000000000000000000000−2i22i20000
χ674-4-44-4-44404004-40-400000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000
χ684-4-44-4-44404004-40-40000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000
χ694-4-44-4-4440-400-4404000000000000000022−22−222222−22−22220000000000000000000000000000000
χ704-4-44-4-4440-400-44040000000000000000−222222−22−222222−220000000000000000000000000000000
χ718-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).